Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural...Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.展开更多
For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the sys...The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear, simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID control scheme.展开更多
The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wav...The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wave functions.Two plasma mediums,namely,the Debye plasma and quantum plasma environments are considered.The screened Coulomb potential(SCP)obtained from Debye-Hückel model is used to represent Debye plasma environments and the exponential cosine screened Coulomb potential(ECSCP)obtained from a modified Debye-Hückel model is used to represent quantum plasma environments.The resonance parameters(resonance positions and widths)are presented in terms of the screening parameters.展开更多
The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simu...The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence(DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.展开更多
Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model(TIAM) is a good starting point for this exploration. To t...Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model(TIAM) is a good starting point for this exploration. To this end,we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit singleparticle impurity Green function under the soft cut-off approximation(SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann–Kittel–Kasuya–Yosida(RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase;while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.展开更多
Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions v...Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.展开更多
As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery...As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.展开更多
A kind of amphiphilic functional monomer was selected to modify polyacrylamide （PAM） or partially hydrolyzed polyacrylamide （HPAM）. The relative properties of the modified polyacrylamide （HM-PAM） and modified pa...A kind of amphiphilic functional monomer was selected to modify polyacrylamide （PAM） or partially hydrolyzed polyacrylamide （HPAM）. The relative properties of the modified polyacrylamide （HM-PAM） and modified partially hydrolyzed polyacrylamide （HM-HPAM） such as radius of gyration （Rg）, hydrodynamic radius （RH）, and radial distribution functions （RDFs） have been studied to find the intrinsic relation between the microstructure of the polymer chain and the intrinsic viscosities with changing the amotmt of modified monomers from 1% to 4%. The simulation results show that, compared to HPAM, HM-HPAM has a better performance in increasing viscosity when the percentage of modified monomers is 2% and has a stronger salt tolerance when the modified monomers is 4%. Furthermore, a complex hydrogen bonding network was revealed with the analysis of radial distribution functions （RDFs） and the pair correlation function was used to investigate the diffusivity of Na^＋ and carbon atoms in the COO^- group.展开更多
Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise wit...Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.展开更多
The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and wei...The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and weighted curve fitting method were presented to make the calculation more simple and accurate. The vertical scales of fluctuation of typical layers of Tianjin Port were calculated based on a number of engineering geotechnical investigation data, which can be guidance to other projects in this area. Meanwhile, the influences of sample interval and type of soil index on the scale of fluctuation were analyzed, according to which, the principle of determining the scale of fluctuation when the sample interval changes was defined. It can be obtained that the scale of fluctuation is the basic attribute reflecting spatial variability of soil, therefore, the scales of fluctuation calculated according to different soil indexes should be basically the same. The non-correlation distance method was improved, and the principle of determining the variance reduction function was also discussed.展开更多
Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion...Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.展开更多
Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to charact...Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.展开更多
The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differenc...The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.展开更多
In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as t...In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.展开更多
The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary ...The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.展开更多
By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlatio...By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.展开更多
The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and ...The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.展开更多
A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simp...A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.展开更多
基金supported by the National Key R&D Program of China under Grant No.2021YFA1400500the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB33000000+1 种基金the National Natural Science Foundation of China under Grant No.12334003the Beijing Municipal Natural Science Foundation under Grant Nos.JQ22001 and QY23014。
文摘Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
文摘The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear, simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID control scheme.
基金Supported by the Natural Science Foundation of Heilongjiang Province(LH2024A025)。
文摘The effects of plasma screening on the ^(1)P^(o) resonance states of H-and He below the n=3 and n=4 thresholds of the respective subsystemsare investigated using the stabilization method and correlated exponential wave functions.Two plasma mediums,namely,the Debye plasma and quantum plasma environments are considered.The screened Coulomb potential(SCP)obtained from Debye-Hückel model is used to represent Debye plasma environments and the exponential cosine screened Coulomb potential(ECSCP)obtained from a modified Debye-Hückel model is used to represent quantum plasma environments.The resonance parameters(resonance positions and widths)are presented in terms of the screening parameters.
文摘The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin.The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence(DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11974420)。
文摘Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model(TIAM) is a good starting point for this exploration. To this end,we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit singleparticle impurity Green function under the soft cut-off approximation(SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann–Kittel–Kasuya–Yosida(RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase;while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.
基金supported by the National Natural Science Foundation of China(No.22273005 and No.22422301)the Innovation Program for Quantum Science and Technology(No.2023ZD0300200)+1 种基金the National Security Academic Foundation(No.U2330201)the Fundamental Research Funds for the Central Universities.
文摘Static disorder plays a crucial role in the electronic dynamics and spec-troscopy of complex molecular sys-tems.Traditionally,obtaining ob-servables averaged over static disor-der requires thousands of realiza-tions via direct sampling of the dis-order distribution,leading to high computational costs.In this work,we extend the auxiliary degree-of-freedom based matrix product state(MPS)method to handle system-bath correlated thermal equilibrium initial states,which can capture static disorder effects using a one-shot quantum dynamical simulation.We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates.Our results show that the one-shot method is very accu-rate with only a moderate increase in MPS bond dimension,thereby significantly reducing computational cost.Moreover,it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost,thus reducing sta-tistical errors.This method provides a broadly useful tool for calculating equilibrium time cor-relation functions in system-bath coupled models with static disorder.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z433)Hunan Provincial Natural Science Foundation of China (Grant No. 09JJ8005)Scientific Research Foundation of Graduate School of Beijing University of Chemical and Technology,China (Grant No. 10Me002)
文摘As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.
基金financially supported by the National Natural Science Foundation of China(No.20904035)
文摘A kind of amphiphilic functional monomer was selected to modify polyacrylamide （PAM） or partially hydrolyzed polyacrylamide （HPAM）. The relative properties of the modified polyacrylamide （HM-PAM） and modified partially hydrolyzed polyacrylamide （HM-HPAM） such as radius of gyration （Rg）, hydrodynamic radius （RH）, and radial distribution functions （RDFs） have been studied to find the intrinsic relation between the microstructure of the polymer chain and the intrinsic viscosities with changing the amotmt of modified monomers from 1% to 4%. The simulation results show that, compared to HPAM, HM-HPAM has a better performance in increasing viscosity when the percentage of modified monomers is 2% and has a stronger salt tolerance when the modified monomers is 4%. Furthermore, a complex hydrogen bonding network was revealed with the analysis of radial distribution functions （RDFs） and the pair correlation function was used to investigate the diffusivity of Na^＋ and carbon atoms in the COO^- group.
文摘Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.
基金Supported by the National Natural Science Foundation of China(No.41272323)Tianjin Natural Science Foundation(No.13JCZDJC 35300)
文摘The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and weighted curve fitting method were presented to make the calculation more simple and accurate. The vertical scales of fluctuation of typical layers of Tianjin Port were calculated based on a number of engineering geotechnical investigation data, which can be guidance to other projects in this area. Meanwhile, the influences of sample interval and type of soil index on the scale of fluctuation were analyzed, according to which, the principle of determining the scale of fluctuation when the sample interval changes was defined. It can be obtained that the scale of fluctuation is the basic attribute reflecting spatial variability of soil, therefore, the scales of fluctuation calculated according to different soil indexes should be basically the same. The non-correlation distance method was improved, and the principle of determining the variance reduction function was also discussed.
文摘Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.
基金supported by the Fundamental Research and Development of Institute of Geophysics,China Earthquake Administration (DQJB07B03)
文摘Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.
基金supported by the Department of Mathematics,Faculty of Science,Mahidol University,Thailand
文摘In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.
文摘The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.
文摘By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.
基金supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.
文摘A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.
